Suppose that a and b are integers, a ≡ 4 (mod 13), and
b ≡ 9 (mod 13). Find the integer c with 0 ≤ c ≤ 12 such
that
a) c ≡ 9a (mod 13).

Question

Suppose that a and b are integers, a ≡ 4 (mod 13), and
b ≡ 9 (mod 13). Find the integer c with 0 ≤ c ≤ 12 such
that
a) c ≡ 9a (mod 13).

ganeshie8 · Answer

$$c \equiv 9a \pmod {13}$$
replace $a$ by $4$ and reduce

anonymous · Answer

But the answer will not be right then.

ganeshie8 · Answer

what do you get after reducing ?

anonymous · Answer

Need to solve it after.

ganeshie8 · Answer

hmm

anonymous · Answer

I did like this. As c = 9a(mod13).
a = 4(mod13), put the value then
c = (36(mod 13))mod13 then how it solve further

ganeshie8 · Answer

reduce 36 in mod 13

ganeshie8 · Answer

36 = 13*2 + 10

so $c\equiv 9a \equiv 9(4) \equiv 36\equiv 10 \pmod{13}$

ganeshie8 · Answer

and 10 is between 0 and 12 so you're done

anonymous · Answer

value of  c is 10, may i right.

mathmath333 · Answer

c = (36(mod 13))mod13 then how it solve further 

$c = ((39-3) (mod 13))mod13 \
c = ((13\times3 -3) (mod 13))mod13 \
c = ((-3) (mod  13))mod13 \
c = (10 )~~(mod13) \
c = (10 )\
$